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8. Sequences and Series
easy
The solution of the equation $1 + a + {a^2} + {a^3} + ....... + {a^x}$ $ = (1 + a)(1 + {a^2})(1 + {a^4})$ is given by $x$ is equal to
A
$3$
B
$5$
C
$7$
D
None of these
Solution
(c) We have $1 + a + {a^2} + ……. + {a^x} = (1 + a)(1 + {a^2})(1 + {a^4})$
$ \Rightarrow $$\frac{{(1 – {a^{x + 1}})}}{{(1 – a)}} = (1 + a)(1 + {a^2}) + (1 + {a^4})$
$\Rightarrow $$(1 – {a^{x + 1}}) = (1 – a)(1 + a)(1 + {a^2})(1 + {a^4})$
$ \Rightarrow $$(1 – {a^{x + 1}}) = (1 – {a^8})$
$ \Rightarrow $$x + 1 = 8$
$ \Rightarrow $$x = 7$.
Standard 11
Mathematics
